RESEARCH PAPER
Near-Resonant Regimes of a Moving Load on a Pre-Stressed Incompressible Elastic Half-Space
1
Department of Mathematical and Computer Modelling, Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, 71 Al-Farabi Ave., 050040, Almaty, Kazakhstan
2
School of Computing and Mathematics, Keele University, Keele, Staffordshire, ST5 5BG, UK
3
Institute for Problems in Mechanical Engineering RAS, 61 Bolshoy Pr., Saint-Petersburg, 199178, Russia
Submission date: 2020-10-15
Acceptance date: 2021-04-19
Online publication date: 2021-05-15
Publication date: 2021-03-01
Acta Mechanica et Automatica 2021;15(1):30-36
KEYWORDS
ABSTRACT
The article is concerned with the analysis of the problem for a concentrated line load moving at a constant speed along the surface of a pre-stressed, incompressible, isotropic elastic half-space, within the framework of the plane-strain assumption. The focus is on the near-critical regimes, when the speed of the load is close to that of the surface wave. Both steady-state and transient regimes are considered. Implementation of the hyperbolic–elliptic asymptotic formulation for the surface wave field allows explicit approximate solution for displacement components expressed in terms of the elementary functions, highlighting the resonant nature of the surface wave. Numerical illustrations of the solutions are presented for several material models.
REFERENCES (40)
1.
Alekseeva L.A., Ukrainets V.N. (2009), Dynamics of an elastic half-space with a reinforced cylindrical cavity under moving loads, Int. Appl. Mech., 45(9), 981-990.
2.
Bratov V. (2011), Incubation time fracture criterion for FEM simulations, Acta Mech. Sin., 27(4), 541.
3.
Cao Y., Xia H., Li Z. (2012), A semi-analytical/FEM model for predicting ground vibrations induced by high-speed train through continuous girder bridge, J. Mech. Sci. Technol., 26, 2485-2496.
4.
Cole J., Huth J. (1958), Stresses produced in a half plane by moving loads, J. Appl. Mech., 25, 433-436.
5.
de Hoop A.T. (2002), The moving-load problem in soil dynamics – the vertical displacement approximation, Wave Motion, 36(4), 335-346.
6.
Dimitrovová Z. (2017), Analysis of the critical velocity of a load moving on a beam supported by a finite depth foundation, Int. J. Solids Struct., 122, 128-147.
7.
Dowaikh M.A., Ogden R.W. (1990), On surface waves and deformations in a pre-stressed incompressible elastic solid, IMA J. Appl. Math., 44, 261-284.
8.
Ege N., Erbaş B., Kaplunov J., Wootton P. (2018), Approximate analysis of surface wave-structure interaction, J. Mech. Mater. Struct., 13(3), 297-309.
9.
Ege N., Şahin O., Erbaş B. (2017), Response of a 3D elastic half-space to a distributed moving load, Hacet J. Math. Stat., 46(5), 817-828.
10.
Erbaş B., Kaplunov J., Nolde E., Palsü M. (2018), Composite wave models for elastic plates, P. Roy. Soc. A-Math. Phy., 474(2214), 1-16.
11.
Erbaş B., Kaplunov J., Palsü M. (2019), A composite hyperbolic equation for plate extension, Mech. Res. Commun., 99, 64-67.
12.
Erbaş B., Kaplunov J., Prikazchikov D.A., Şahin O. (2017), The near-resonant regimes of a moving load in a three-dimensional problem for a coated elastic half-space, Math. Mech. Solids, 22(1), 89–100.
13.
Fryba L. (1999), Vibration of solids and structures under moving loads, 3rd ed, Thomas Telford, London.
14.
Fu Y., Kaplunov J., Prikazchikov D. (2020), Reduced model for the surface dynamics of a generally anisotropic elastic half-space, P. Roy. Soc. A-Math. Phy., 476(2234), 1-19.
15.
Gakenheimer D.C., Miklowitz J. (1969), Transient excitation of an elastic half space by a point load traveling on the surface, J. Appl. Mech., 36(3), 505-515.
16.
Gent A.N. (1996), A new constitutive relation for rubber, Rubber Chem. Technol., 69(1), 59-61.
17.
Goldstein R.V. (1965), Rayleigh waves and resonance phenomena in elastic bodies, J. Appl. Math. Mech. (PMM), 29(3), 516-525.
18.
Gourgiotis P.A., Piccolroaz A. (2014), Steady-state propagation of a mode II crack in couple stress elasticity, Int. J. Fract., 188(2), 119-145.
19.
Kaplunov J., Nolde E., Prikazchikov D.A. (2010a), A revisit to the moving load problem using an asymptotic model for the Rayleigh wave, Wave Motion, 47, 440-451.
20.
Kaplunov J., Prikazchikov D., Sultanova L. (2019), Rayleigh-type waves on a coated elastic half-space with a clamped surface, Phil. Trans. Roy. Soc. A, 377(2156), 1-15.
21.
Kaplunov J., Prikazchikov D.A. (2017), Asymptotic theory for Rayleigh and Rayleigh-type waves, Adv. Appl. Mech., 50, 1-106.
22.
Kaplunov J., Prikazchikov D.A., Erbaş B., Şahin O. (2013), On a 3D moving load problem for an elastic half space, Wave Motion, 50(8), 1229-1238.
23.
Kaplunov J., Voloshin V., Rawlins A.D. (2010b), Uniform asymptotic behaviour of integrals of Bessel functions with a large parameter in the argument, Quart. J. Mech. Appl. Math., 63(1), 57-72.
24.
Khajiyeva L.A., Prikazchikov D.A., Prikazchikova L.A. (2018), Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space, Mech. Res. Commun., 92, 49-53.
25.
Krylov V.V. (1996), Vibrational impact of high-speed trains. I. Effect of track dynamics, J. Acoust. Soc. Am., 100(5), 3121-3134.
26.
Kumar R., Vohra R. (2020), Steady state response due to moving load in thermoelastic material with double porosity, Mater. Phys. Mech., 44(2), 172-185.
27.
Lefeuve-Mesgouez G., Le Houédec D., Peplow A.T. (2000), Ground vibration in the vicinity of a high-speed moving harmonic strip load, J. Sound Vib., 231(5), 1289-1309.
28.
Lu T., Metrikine A.V., Steenbergen M.J.M.M. (2020), The equivalent dynamic stiffness of a visco-elastic half-space in interaction with a periodically supported beam under a moving load, Europ. J. Mech.-A/Solids, 84, 104065.
29.
Mishuris G., Piccolroaz A., Radi E. (2012), Steady-state propagation of a Mode III crack in couple stress elastic materials, Int. J. Eng. Sci., 61, 112-128.
31.
Payton R.G. (1967), Transient motion of an elastic half-space due to a moving surface line load, Int. J. Eng. Sci., 5(1), 49-79.
32.
Pucci E., Saccomandi G. (2002), A note on the Gent model for rubber-like materials, Rubber Chem. Technol., 75(5), 839-852.
33.
Smirnov V., Petrov Yu.V., Bratov V. (2012), Incubation time approach in rock fracture dynamics, Sci. China Phys., Mech. Astr., 55(1), 78-85.
34.
Sun Z., Kasbergen C., Skarpas A., Anupam K., van Dalen K.N., Erkens S.M. (2019), Dynamic analysis of layered systems under a moving harmonic rectangular load based on the spectral element method, Int. J. Solids Struct., 180, 45-61.
35.
van Dalen K.N., Tsouvalas A., Metrikine A.V., Hoving J.S. (2015), Transition radiation excited by a surface load that moves over the interface of two elastic layers, Int. J. Solids Struct., 73, 99-112.
36.
Wang F., Han X., Ding T. (2021), An anisotropic layered poroelastic half-space subjected to a moving point load, Soil Dyn. Earth. Eng., 140, 106427.
37.
Wang Y., Zhou A., Fu T., Zhang W. (2020), Transient response of a sandwich beam with functionally graded porous core traversed by a non-uniformly distributed moving mass, Int. J. Mech. Mater. Design, 16(3), 519-540.
38.
Wootton P.T., Kaplunov J., Colquitt D.J. (2019), An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces, P. Roy. Soc. A-Math. Phy., 475(2227), 1-18.
39.
Wootton P.T., Kaplunov J., Prikazchikov D. (2020), A second-order asymptotic model for Rayleigh waves on a linearly elastic half plane, IMA J. Appl. Math., 85, 113-131.
40.
Zhou L., Wang S., Li L., Fu Y. (2018), An evaluation of the Gent and Gent-Gent material models using inflation of a plane membrane, Int. J. Mech. Sci., 146-147, 39-48.
| eISSN: | 2300-5319 |
| ISSN: | 1898-4088 |
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